Adaptive Row Selection Meets Asynchrony in Randomized Kaczmarz

[2607.08313] Adaptive Row Selection Meets Asynchrony in Randomized Kaczmarz Skip to main content Search Submit Donate Log in Computer Science > Distributed, Parallel, and Cluster Computing arXiv:2607.08313 (cs) [Submitted on 9 Jul 2026 ( v1 ), last revised 22 Aug 2026 (this version, v2)] Title: Adaptive Row Selection Meets Asynchrony in Randomized Kaczmarz Authors: Evan Coleman View PDF HTML (experimental) Abstract: Randomized Kaczmarz is a natural fit for large sparse least-squares and tomographic reconstruction, and adaptive row selection can reduce iteration counts. However, deploying adaptive selection on a shared-memory machine means sampling from a residual that lock-free workers are concurrently modifying, often using stale data. We present the first systematic study of this regime: residual-weighted and greedy Kaczmarz under asynchronous execution, measured across 339 runs on a 96-core node with realized (not injected) delays. Four findings carry directly to practice. (i) Stability is governed by a boundary $\ell^*(T)$ between sampling aggressiveness and thread count; below it, more aggressive sampling is strictly better, so one should tune to just inside the cliff. (ii) Threshold-greedy selection (the standard accelerated rule) is unstable at high thread counts, diverging almost immediately. (iii) Under-relaxation buys back the cliff at a predictable cost, giving a usable safety knob. (iv) Consistent-snapshot reads admit a rare, scheduling-dependent divergence that live (inconsistent) reads never exhibited; live reads also cost less per step, making them the right default. We validate the implementation against published sequential results and outline the distributed two-level sampler these measurements motivate. Subjects: Distributed, Parallel, and Cluster Computing (cs.DC) ; Numerical Analysis (math.NA) Cite as: arXiv:2607.08313 [cs.DC] (or arXiv:2607.08313v2 [cs.DC] for this version) https://doi.org/10.48550/arXiv.2607.08313 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.48550/arXiv.2607.08313 Focus to learn more DOI(s) linking to related resources Submission history From: Evan Coleman [ view email ] [v1] Thu, 9 Jul 2026 09:55:19 UTC (353 KB) [v2] Sat, 22 Aug 2026 00:48:35 UTC (354 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.DC < prev | next > new | recent | 2026-07 Change to browse by: cs cs.NA math math.NA References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• Adaptive Row Selection Meets Asynchrony in Randomized Kaczmarz#665841
• Adaptive Row Selection Meets Asynchrony in Randomized Kaczmarz#353029
• On the Subsample Size of Quantile-Based Randomized Kaczmarz#684245
• On the Subsample Size of Quantile-Based Randomized Kaczmarz#682470
• A Tale of Two Learning Algorithms: Multiple Stream Random Walk and Asynchronous Gossip#149258